Gapless non-hydrodynamic modes in relativistic kinetic theory

Abstract

We provide rigorous criteria to determine whether the non-hydrodynamic sector of a relativistic kinetic theory is gapless. These general criteria apply to both Boltzmann's equation and approximate models thereof, provided that the latter are consistent with thermodynamic principles. As an application of these criteria, we prove that the non-hydrodynamic sector is gapless whenever the scattering cross-section decays to zero at large energies. Physically, this happens because, if particles with very high energy (compared to the temperature) are free streaming, we can use them to build hot non-hydrodynamic waves, which live longer than any hydrodynamic wave. Since many standard cross-sections in quantum field theory vanish at high energies, the existence of these non-thermal long-lived waves is a rather general feature of relativistic systems.